\relax 
\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
\global\let\oldcontentsline\contentsline
\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
\global\let\oldnewlabel\newlabel
\gdef\newlabel#1#2{\newlabelxx{#1}#2}
\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
\AtEndDocument{\ifx\hyper@anchor\@undefined
\let\contentsline\oldcontentsline
\let\newlabel\oldnewlabel
\fi}
\fi}
\global\let\hyper@last\relax 
\gdef\HyperFirstAtBeginDocument#1{#1}
\providecommand\HyField@AuxAddToFields[1]{}
\@writefile{toc}{\beamer@endinputifotherversion {3.10pt}}
\@writefile{nav}{\beamer@endinputifotherversion {3.10pt}}
\select@language{english}
\@writefile{toc}{\select@language{english}}
\@writefile{lof}{\select@language{english}}
\@writefile{lot}{\select@language{english}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{1}{1/1}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {1}{1}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{2}{2/2}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {2}{2}}}
\@writefile{toc}{\beamer@sectionintoc {1}{Over view}{3}{0}{1}}
\@writefile{nav}{\headcommand {\sectionentry {1}{Over view}{3}{Over view}{0}}}
\@writefile{nav}{\headcommand {\beamer@sectionpages {1}{2}}}
\@writefile{nav}{\headcommand {\beamer@subsectionpages {1}{2}}}
\@writefile{nav}{\headcommand {\slideentry {1}{0}{3}{3/3}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {3}{3}}}
\@writefile{nav}{\headcommand {\slideentry {1}{0}{4}{4/4}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {4}{4}}}
\@writefile{toc}{\beamer@sectionintoc {2}{Introduction}{5}{0}{2}}
\@writefile{nav}{\headcommand {\sectionentry {2}{Introduction}{5}{Introduction}{0}}}
\@writefile{nav}{\headcommand {\beamer@sectionpages {3}{4}}}
\@writefile{nav}{\headcommand {\beamer@subsectionpages {3}{4}}}
\@writefile{nav}{\headcommand {\slideentry {2}{0}{5}{5/5}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {5}{5}}}
\@writefile{nav}{\headcommand {\slideentry {2}{0}{6}{6/6}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {6}{6}}}
\@writefile{nav}{\headcommand {\slideentry {2}{0}{7}{7/7}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {7}{7}}}
\@writefile{toc}{\beamer@sectionintoc {3}{Preliminaries and notation}{8}{0}{3}}
\@writefile{nav}{\headcommand {\sectionentry {3}{Preliminaries and notation}{8}{Preliminaries and notation}{0}}}
\@writefile{nav}{\headcommand {\beamer@sectionpages {5}{7}}}
\@writefile{nav}{\headcommand {\beamer@subsectionpages {5}{7}}}
\@writefile{toc}{\beamer@subsectionintoc {3}{1}{Basic notation}{8}{0}{3}}
\@writefile{nav}{\headcommand {\beamer@subsectionentry {0}{3}{1}{8}{Basic notation}}\headcommand {\beamer@subsectionpages {8}{7}}}
\@writefile{nav}{\headcommand {\slideentry {3}{1}{1}{8/8}{Basic notation}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {8}{8}}}
\@writefile{nav}{\headcommand {\slideentry {3}{1}{2}{9/9}{Basic notation}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {9}{9}}}
\@writefile{toc}{\beamer@subsectionintoc {3}{2}{Orientable}{10}{0}{3}}
\@writefile{nav}{\headcommand {\beamer@subsectionentry {0}{3}{2}{10}{Orientable}}\headcommand {\beamer@subsectionpages {8}{9}}}
\@writefile{nav}{\headcommand {\slideentry {3}{2}{1}{10/10}{Orientable}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {10}{10}}}
\@writefile{nav}{\headcommand {\slideentry {3}{2}{2}{11/11}{Orientable}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {11}{11}}}
\@writefile{nav}{\headcommand {\slideentry {3}{2}{3}{12/12}{Orientable}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {12}{12}}}
\@writefile{nav}{\headcommand {\slideentry {3}{2}{4}{13/13}{Orientable}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {13}{13}}}
\@writefile{nav}{\headcommand {\slideentry {3}{2}{5}{14/14}{Orientable}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {14}{14}}}
\@writefile{nav}{\headcommand {\slideentry {3}{2}{6}{15/15}{Orientable}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {15}{15}}}
\@writefile{nav}{\headcommand {\slideentry {3}{2}{7}{16/16}{Orientable}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {16}{16}}}
\@writefile{toc}{\beamer@sectionintoc {4}{Orientability issues}{17}{0}{4}}
\@writefile{nav}{\headcommand {\sectionentry {4}{Orientability issues}{17}{Orientability issues}{0}}}
\@writefile{nav}{\headcommand {\beamer@sectionpages {8}{16}}}
\@writefile{nav}{\headcommand {\beamer@subsectionpages {10}{16}}}
\@writefile{toc}{\beamer@subsectionintoc {4}{1}{over view of this section}{17}{0}{4}}
\@writefile{nav}{\headcommand {\beamer@subsectionentry {0}{4}{1}{17}{over view of this section}}\headcommand {\beamer@subsectionpages {17}{16}}}
\@writefile{nav}{\headcommand {\slideentry {4}{1}{1}{17/17}{over view of this section}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {17}{17}}}
\@writefile{toc}{\beamer@subsectionintoc {4}{2}{Continuous line fields on arbitrary domains}{18}{0}{4}}
\@writefile{nav}{\headcommand {\beamer@subsectionentry {0}{4}{2}{18}{Continuous line fields on arbitrary domains}}\headcommand {\beamer@subsectionpages {17}{17}}}
\@writefile{nav}{\headcommand {\slideentry {4}{2}{1}{18/18}{Continuous line fields on arbitrary domains}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {18}{18}}}
\@writefile{nav}{\headcommand {\slideentry {4}{2}{2}{19/19}{Continuous line fields on arbitrary domains}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {19}{19}}}
\@writefile{nav}{\headcommand {\slideentry {4}{2}{3}{20/20}{Continuous line fields on arbitrary domains}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {20}{20}}}
\@writefile{nav}{\headcommand {\slideentry {4}{2}{4}{21/21}{Continuous line fields on arbitrary domains}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {21}{21}}}
\@writefile{nav}{\headcommand {\slideentry {4}{2}{5}{22/22}{Continuous line fields on arbitrary domains}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {22}{22}}}
\@writefile{toc}{\beamer@subsectionintoc {4}{3}{Arbitrary line fields on simply-connected domains}{23}{0}{4}}
\@writefile{nav}{\headcommand {\beamer@subsectionentry {0}{4}{3}{23}{Arbitrary line fields on simply-connected domains}}\headcommand {\beamer@subsectionpages {18}{22}}}
\@writefile{nav}{\headcommand {\slideentry {4}{3}{1}{23/23}{Arbitrary line fields on simply-connected domains}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {23}{23}}}
\@writefile{toc}{\beamer@sectionintoc {5}{Analytic orientability criteria in 2D}{24}{0}{5}}
\@writefile{nav}{\headcommand {\sectionentry {5}{Analytic orientability criteria in 2D}{24}{Analytic orientability criteria in 2D}{0}}}
\@writefile{nav}{\headcommand {\beamer@sectionpages {17}{23}}}
\@writefile{nav}{\headcommand {\beamer@subsectionpages {23}{23}}}
\@writefile{toc}{\beamer@subsectionintoc {5}{1}{Preliminary}{24}{0}{5}}
\@writefile{nav}{\headcommand {\beamer@subsectionentry {0}{5}{1}{24}{Preliminary}}\headcommand {\beamer@subsectionpages {24}{23}}}
\@writefile{nav}{\headcommand {\slideentry {5}{1}{1}{24/24}{Preliminary}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {24}{24}}}
\@writefile{nav}{\headcommand {\slideentry {5}{1}{2}{25/25}{Preliminary}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {25}{25}}}
\@writefile{nav}{\headcommand {\slideentry {5}{1}{3}{26/26}{Preliminary}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {26}{26}}}
\@writefile{toc}{\beamer@subsectionintoc {5}{2}{Important Propostions}{27}{0}{5}}
\@writefile{nav}{\headcommand {\beamer@subsectionentry {0}{5}{2}{27}{Important Propostions}}\headcommand {\beamer@subsectionpages {24}{26}}}
\@writefile{nav}{\headcommand {\slideentry {5}{2}{1}{27/27}{Important Propostions}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {27}{27}}}
\@writefile{nav}{\headcommand {\slideentry {5}{2}{2}{28/28}{Important Propostions}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {28}{28}}}
\@writefile{toc}{\beamer@subsectionintoc {5}{3}{The final lemmas of this section}{29}{0}{5}}
\@writefile{nav}{\headcommand {\beamer@subsectionentry {0}{5}{3}{29}{The final lemmas of this section}}\headcommand {\beamer@subsectionpages {27}{28}}}
\@writefile{nav}{\headcommand {\slideentry {5}{3}{1}{29/29}{The final lemmas of this section}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {29}{29}}}
\@writefile{nav}{\headcommand {\slideentry {5}{3}{2}{30/30}{The final lemmas of this section}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {30}{30}}}
\@writefile{nav}{\headcommand {\slideentry {5}{3}{3}{31/31}{The final lemmas of this section}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {31}{31}}}
\@writefile{toc}{\beamer@sectionintoc {6}{Enegy minimizing}{32}{0}{6}}
\@writefile{nav}{\headcommand {\sectionentry {6}{Enegy minimizing}{32}{Enegy minimizing}{0}}}
\@writefile{nav}{\headcommand {\beamer@sectionpages {24}{31}}}
\@writefile{nav}{\headcommand {\beamer@subsectionpages {29}{31}}}
\@writefile{nav}{\headcommand {\slideentry {6}{0}{4}{32/32}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {32}{32}}}
\@writefile{nav}{\headcommand {\slideentry {6}{0}{5}{33/33}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {33}{33}}}
\@writefile{nav}{\headcommand {\slideentry {6}{0}{6}{34/34}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {34}{34}}}
\@writefile{nav}{\headcommand {\beamer@partpages {1}{34}}}
\@writefile{nav}{\headcommand {\beamer@subsectionpages {32}{34}}}
\@writefile{nav}{\headcommand {\beamer@sectionpages {32}{34}}}
\@writefile{nav}{\headcommand {\beamer@documentpages {34}}}
\@writefile{nav}{\headcommand {\def \inserttotalframenumber {34}}}
